Figure P3.17 shows a free-body diagram of an inverted pendulum, mounted on a cart with a mass, M. The pendulum has a point mass, m, concentrated at the upper end of a rod with zero mass, a length, I, and a frictionless hinge. A motor drives the cart, applying a horizontal force, u(t). A gravity force, mg, acts on m at all times. The pendulum angle relative to the y-axis,
However, since x0= 0 and u0= 0, then let:
where
Assuming the output to be the horizontal position of
Given that: M = 2.4 kg, m = 0.23 kg, MATLAB ML l = 0.36 m, g = 9.81 m/s2, use MATLAB to ?nd the transfer function, G(s) = Y(s)/U(s) = Xm(s)/U(s).
FIGURE P3.17 Motor-driven inverted pendulum can system15
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